Spectrometers for the spectral decomposition and measurement of light from emission processes, produced by evaporation and excitation of materials in hot plasmas (arc discharge in air atmosphere spark discharge in argon, ICP, lasers etc.) are known in many diverse embodiments.
Generally spectrometers comprise a light inlet opening which is punctiform or linear and can be designed as single or multiple opening. The light to be decomposed either passes through a light guide or a light guide bundle from the location of plasma generation to the light inlet opening which is then potentially far removed (10 m and more are possible for wavelengths from about 230 mm) or goes directly from an outwardly closed, possibly argon- or nitrogen-gas-flushed or evacuated light channel direction from the location of the plasma generation to the light inlet opening. In the latter case, the optical system must be located very close to (at most a few decimeters away from) the location of the plasma generation and be aligned relative thereto.
The orientation and extension of the non-punctiform light inlet opening plays a role in the dimensioning and positioning of imaging elements and diaphragms in the light channel between light source and light inlet opening since it must be ensured that the analytically relevant plasma regions can be completely accommodated by the optical system.
From the light inlet opening, the light to be decomposed passes to one or more simultaneously or successively operating imaging and dispersive elements. The dispersive elements can be prisms or mechanically or holographically produced diffraction gratings. Spherical or aspherical mirrors are used as imaging elements.
The structure of the optical system is simplified when using reflection-coated, spherical and concave diffraction gratings since in such systems dispersion and imaging is accomplished by one and the same optical element.
Depending on the shape and density of the diffracting structure applied to the spherical surface of the diffraction grating (shape and spacing of the grating lines), the radius of curvature of the spherical surface of the diffraction grating and the distance of the light inlet opening from the centre of symmetry of the grating lines on the grating surface (grating central point), the so-called inlet back focal length, the spectral lines of certain well-known wavelengths characteristic of a material to be analysed are found in the structure of the optical system at certain diffraction angles which can be calculated with the aid of the so-called grating equation and at certain diffraction-angle-dependent distances from the grating central point (outlet back focal lengths).
The grating equation:nGλ=sin α+sin β  (1)describes which wavelength λ appears in which diffraction order n at given line density or grating constant C (given in lines per mm) at which diffraction angle β, when the angle of incidence α of the light to be decomposed is known. The angles are here plotted on the so-called grating normal. This is the connecting line between grating central point and curvature central point of the grating surface.
The curve that describes the angle- and distance-dependent position of spectral lines of given wavelengths relative to the grating central point is called the focal curve. The best known special case of a focal curve is the Rowland circle in the so-called Paschen-Runge mounting of a concave grating. In this case, grating central point, light inlet opening and detector unit are located tangentially arranged on a circle whose diameter corresponds to the radius of curvature of the concave grating and whose plane is designated as dispersion plane
In contrast to the Paschen-Runge mounting, the focal curve of a flat field grating runs flatter or sometimes in an S-shape.
The generally valid formula for the profile of focal curve of Rowland circle and flat field gratings in the dispersion plane is the back focus equation:
                                                                        cos                2                            ⁢              α                                      L              A                                -                                    cos              ⁢                                                          ⁢              α                        R                    +                                                    cos                2                            ⁢              β                                      L              B                                -                                    cos              ⁢                                                          ⁢              β                        R                    -                      n            ⁢                                                  ⁢            λ            ⁢                                                  ⁢            K                          =        0                            (        2        )            where:    α is the angle of incidence;    β is the diffraction angle;    LA is the inlet back focal length;    LB is the outlet back focal length;    R is the grating radius (radius of curvature of the spherical grating surface);    n is the diffraction order (integer, positive or negative);    λ is the wavelength (at diffraction angle β);    K is the spherical grating constant, depending on line shape.
From the back focus equation (2) it follows for K=0 (Rowland circle grating) that all the outlet back focal lengths must lie on one circle if the inlet back focal length and the grating central point lie on the same circle. In addition, it can be generally derived that a shortening or lengthening of the inlet back focal length by an amount ΔL, to a good approximation changes all the outlet back focal lengths by the same amount but with opposite sign.
Since the materials of which spectrometers are usually constructed usually do not have negligible coefficients of thermal expansion, temperature fluctuations have an influence on the measurement. The length extension of a given material with a temperature difference ΔT is determined by the corresponding coefficient of linear thermal expansion α:l2=l1(1+αΔT)  (3)where:    ΔT is the temperature difference;    l1 is the initial length;    l2 is the end length;    α is the coefficient of linear thermal expansion.
In a spectrometer the thermal expansion has various consequences. If a diffraction grating is applied to a substrate, which has a non-negligible coefficient of thermal expansion α, the grating constant varies with the temperature and the diffraction angle is therefore temperature-dependent (cf. grating equation (1)). This effect is manifest in a wavelength-dependent positional drift of the optical system.
When detecting the (complete) spectrum with spatially resolving sensors (e.g. CCD or CMOS detectors), the positional drift can easily be compensated by means of a superpositionable drift reference spectrum within the framework of a reference measurement. A software-dependent spectrum tracking can also be implemented by means of the continuous observation of spectral structures or sections which continually reoccur and are comparable for a plurality of samples. Such methods have been available for many years in the prior art and in a plurality of spectrometers.
Tracking the detector unit tangentially to the focal curve is feasible and is described for individual detectors in DE 10 2004 061 178 A1.
EP 1 041 372 A1 proposes a solution in which the detector unit of a spectrometer is mounted on a support material having a high coefficient of thermal expansion and is fixed to the main optical body so that when thermal expansion occurs, the centre of the detector unit follows the wavelength-dependent spectral shift resulting from the change in the grating constant to a good approximation. However, a change in the focal position is not compensated or eliminated in this structure since the measuring task to be fulfilled does not require any exactly held focal position.
As is described in DE 10 2004 061 178 A1 and generally known, the focusing of an optical system is part of its basic alignment which can only be accomplished by means of the movement of the light inlet opening if the detector units are correctly position on the (instantaneous) focal curve of the system. However, if the back focal lengths vary as a function of the temperature, because the coefficients of thermal expansion of the materials used cannot be neglected (cf. back focus equation (2)), the optical system varies its focal curve (defocusing) as a function of temperature and thereby loses spectral resolution since with increasing temperature all the spacings in the system enlarge but the outlet back focal length must become smaller if the back focus equation is to be satisfied and therefore the focal position or spectral resolution should be preserved with increasing inlet back focal length.
To compensate for the effect just described, it is suggested in DE 10 2004 061 178 A1 to re-focus the light inlet opening by means of actuators and thus optimise the sharpness of the image. The optimum can then be found and re-adjusted by means of an algorithm within the framework of a reference measurement. Alternatively spectrometers can be dimensioned so that within a predefined temperature interval, only small changes in the spectral resolution of the system occur as a result of defocusing due to thermal expansion. A condition for the permissible defocusing at a given maximum temperature, is remaining within the depth of focus interval of the optical system:
                              t          w                =                              n            ⁢                                                  ⁢            λ                                A            2                                              (        4        )            where:    tw is the wave-optical depth of focus;    n is the diffraction order;    λ is the wavelength;    A is the aperture (depending on the grating illumination and the grating radius).
By selecting materials having a very low or no coefficient of thermal expansion α and/or keeping the operating temperature T of the optical system constant (thermostatic control) and/or active tracking either of the light inlet opening or of the detector unit or both assemblies by means of linear motors, piezo-actuators and the like, the consequences of the thermal expansion can be limited or completely eliminated if the entire system could or must be exposed to a broad temperature interval.
In practice, analytical devices fitted with spectrometers, in particular portable and mobile systems which possibly should also be battery-operated, are subject to some restrictions. Portable systems should be as light as possible and nevertheless have a sufficient and as far as possible constant spectral resolution capacity. Waiting times for switching a system on again after longer operating pauses should be as short as possible.
Reference measurements during measurement operation are perceived as disturbing and should therefore be restricted to a minimum. However, complex mechanical actuator-based tracking systems are potentially liable to breakdown. In addition, they are relatively expensive and increase the overall size of spectrometers fitted with them.
A further disadvantage of known thermostatic controls of optical systems of spectrometers is that they shorten the operating life in battery operation of a spectrometer, in some cases even quite considerably.
Special alloys or ceramics having very low, almost negligible coefficients of thermal expansion are very expensive and additionally usually very difficult to process. Non-metallic materials are usually only available as thin plate material so that frequently not all the required processings can be carried out problem-free such as, for example, the manufacture of clearances and threaded bores. The manufacture of compact spatial structures is considerably simpler with metal materials but the said special alloys are not only expensive but also very heavy and therefore unsuitable for portable systems.